On Degrees of Modular Common Divisors and the Big Prime gcd Algorithm
We consider a few modifications of the Big prime modular gcd algorithm for polynomials in Z[x]. Our modifications are based on bounds of degrees of modular common divisors of polynomials, on estimates of the number of prime divisors of a resultant, and on finding preliminary bounds on degrees of com...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2016/3262450 |
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| author | Vahagn Mikaelian |
| author_facet | Vahagn Mikaelian |
| author_sort | Vahagn Mikaelian |
| collection | DOAJ |
| description | We consider a few modifications of the Big prime modular gcd algorithm for polynomials in Z[x]. Our modifications are based on bounds of degrees of modular common divisors of polynomials, on estimates of the number of prime divisors of a resultant, and on finding preliminary bounds on degrees of common divisors using auxiliary primes. These modifications are used to suggest improved algorithms for gcd calculation and for coprime polynomials detection. To illustrate the ideas we apply the constructed algorithms on certain polynomials, in particular on polynomials from Knuth’s example of intermediate expression swell. |
| format | Article |
| id | doaj-art-746d494bc7ac4dcbbb4e42696f761c6d |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-746d494bc7ac4dcbbb4e42696f761c6d2025-08-20T03:33:53ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252016-01-01201610.1155/2016/32624503262450On Degrees of Modular Common Divisors and the Big Prime gcd AlgorithmVahagn Mikaelian0Yerevan State University, Alex Manoogian 1, 0025 Yerevan, ArmeniaWe consider a few modifications of the Big prime modular gcd algorithm for polynomials in Z[x]. Our modifications are based on bounds of degrees of modular common divisors of polynomials, on estimates of the number of prime divisors of a resultant, and on finding preliminary bounds on degrees of common divisors using auxiliary primes. These modifications are used to suggest improved algorithms for gcd calculation and for coprime polynomials detection. To illustrate the ideas we apply the constructed algorithms on certain polynomials, in particular on polynomials from Knuth’s example of intermediate expression swell.http://dx.doi.org/10.1155/2016/3262450 |
| spellingShingle | Vahagn Mikaelian On Degrees of Modular Common Divisors and the Big Prime gcd Algorithm International Journal of Mathematics and Mathematical Sciences |
| title | On Degrees of Modular Common Divisors and the Big Prime gcd Algorithm |
| title_full | On Degrees of Modular Common Divisors and the Big Prime gcd Algorithm |
| title_fullStr | On Degrees of Modular Common Divisors and the Big Prime gcd Algorithm |
| title_full_unstemmed | On Degrees of Modular Common Divisors and the Big Prime gcd Algorithm |
| title_short | On Degrees of Modular Common Divisors and the Big Prime gcd Algorithm |
| title_sort | on degrees of modular common divisors and the big prime gcd algorithm |
| url | http://dx.doi.org/10.1155/2016/3262450 |
| work_keys_str_mv | AT vahagnmikaelian ondegreesofmodularcommondivisorsandthebigprimegcdalgorithm |